Keemic family: Difference between revisions

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 {{Technical data page}}
-The '''keemic family''' is a family of [[rank-3 temperament]]s which [[tempering out|temper out]] the [[keema]] ({{monzo|legend=1| -5 -3 3 1 }}, [[ratio]]: 875/864).
+The '''keemic family''' is a family of [[rank-3 temperament]]s which [[tempering out|temper out]] the [[keema]] ({{monzo|legend=1| -5 -3 3 1 }}, [[ratio]]: 875/864). For [[rank-2 temperament]]s, see [[keemic temperaments]].
+== Keemic ==
+Keemic, also known as ''supermagic'' in earlier materials, has the same lattice structure as [[5-limit]] JI, and [[7/4]] is found by a stack of three [[~]][[6/5]]'s.
-== Supermagic ==
 [[Subgroup]]: 2.3.5.7
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 Scales: [[supermagic15]]
-== Undecimal supermagic ==
+== Undecimal keemic ==
-{{See also| Ptolemismic clan #Supermagic }}
+{{See also| Ptolemismic clan #Keemic }}
+Keemic is naturally an [[11-limit]] temperament due to the identity 875/864 = ([[100/99]])⋅([[385/384]]). This identifies a stack of two ~6/5's as ~[[16/11]].
 [[Subgroup]]: 2.3.5.7.11
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 == Supernatural ==
+Supernatural uses the same mapping as [[7-limit]] [[magic]] with an independent generator for prime 11.
 [[Subgroup]]: 2.3.5.7.11
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 * CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.1532{{c}}, ~11/8 = 548.2678{{c}}
-{{Optimal ET sequence|legend=1| 19, 22f, 38df, 41, 60e, 79d, 101cd }}
+{{Optimal ET sequence|legend=0| 19, 22f, 38df, 41, 60e, 79d, 101cd }}
 Badness (Sintel): 1.07
+[[Category:Keemic family| ]] <!-- main article -->
 [[Category:Temperament families]]
-[[Category:Pages with mostly numerical content]]
+[[Category:Catalogs of rank-3 temperaments]]
-[[Category:Keemic family| ]] <!-- main article -->
-[[Category:Supermagic]]
-[[Category:Rank 3]]